It's after the resignation of Edouard Philippe who has been in the post for three years.
Mr Castex, 55, is relatively unknown in France, although he is a senior civil servant.
The new Prime Minister has been a key player in the government's response to the Covid-19 pandemic.
Isaias weakens to Category 1 hurricane after Florida landfall, NHC says
Hurricane Isaias has rapidly lost windspeed, weakening into a Category 1 event after making landfall near Destin, Florida, the US National Hurricane Centre said, but warned of danger from storm surges and floods as power links snapped.
India detains protesters, locks down Delhi ahead of rally against election chief
Police in the Indian capital detained scores of protesters on Saturday amid patrols by thousands of security forces, with travel and telecoms links suspended, in a lockdown to stop a youth protest asking the election chief to quit.
Magnitude 7.7 quake shakes Panama, canal operations normal
A strong 7.7 magnitude earthquake has struck near the southern coast of Panama on Friday at a depth of 10km, according to the US Geological Survey, yet no damage was initially reported, and the Panama Canal Authority said the waterway was operating normally.
US imposes sanctions on International Criminal Court
US President Donald Trump's administration has imposed sanctions on the International Criminal Court on Friday, hours after one of its former judges won the Nobel Peace Prize, putting Washington on a diplomatic collision course with European allies.
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